The high speed computation of the correlation between audio or radio frequency signals is an important signal processing operation. An optically implemented analog device which accomplishes this is described in this disclosure. Other optically implemented devices have been described previously. In one reference the waveform of a reference radio frequency signal is displayed as a spatially varying stationary refractive index pattern in a surface acoustic wave acousto-optic device. The electro-optic effect is used to produce the index changes; the electric fields are produced with programmed voltages on finger electrodes. See, "An Integrated Optical Spatial Filter," by C. M. Verber, R. P. Kenan and J. R. Bush, Optics Communications, Volume 34, Number 1, pages 32-34 (1980). In another reference, an index of refraction pattern is created in the same type of acousto-optic device by the interaction of the moving refractive index pattern produced by the acoustic wave and a short duration intense pulse of coherent illumination. The effect is to convert the moving pattern at the moment of illumination into a stationary pattern. See U.S. Pat. No. 4,139,277 to Berg et al, and "A New Acoustophotorefractive Effect in Lithium Niobate", by N. J. Berg, B. J. Udelson, and J. N. Lee, Applied Physics Letters, Volume 31, Number 9, pages 555-557, (November, 1977). In these devices the correlation is obtained from a coherent optical input after being diffracted (simultaneously) by the stationary pattern stored in the optical substrate of the device, and by a moving pattern produced with a second signal.
The present invention is a device which differs from these references in the method of storing the reference signal and in the method of the analog computation of the correlation. The reference signal is not stored as a refractive index pattern within the substrate of an acousto-optic device. Rather the moving pattern created by the reference signal diffracts a short duration pulse coherent optical input, producing an optical field containing the signal phase and amplitude at the moment of illumination. This field is then incident on a photorefractive crystal. This input produces in the crystal a volume phase hologram which persists for some interval of time. The hologram is of a kind which reconstructs, not the original field, but the optical phase conjugate of this field. To obtain the correlation optical output this phase conjugate field is reconstructed. It passes back through the acousto-optic device where it is diffracted by a second signal. The electrical signal proportional to the correlation function is then obtained from the optical output using a lens and a photodiode.
This analog computation method of the present invention is related to a holographic method for aberration removal. In this process a hologram, produced in a photographic medium, is that of an optical field distorted by a phase distorting object such as pebble surface glass. From this hologram, a phase conjugate of the input optical field is reconstructed. This optical field passes back through the phase object, where the object and hologram, are repositioned exactly as they were at the time the hologram was made. The effect of the distorter is then to remove the distortions in the phase conjugate field. This field, a back propagating version of the original distorted field is now observed undistorted. See, "Holographic Imagery Through Diffusing Media," Journal of the Optical Society of America, Volume 56, Number 4, page 523 Emmet Leith and Juris Upatneik, Journal (April 1966). In the present invention there is an analog to the distorter in the form of the acousto-optic device with an index of refraction pattern produced by the reference electrical signal. A phase conjugating phase volume hologram is produced in the photorefractive crystal. A reconstructed phase conjugate field passes back through the optical device where it is diffracted by a new index of refraction pattern produced by a second electrical input. If the second input signal is identical to the first there will appear in the acousto-optic device a second index of refraction pattern identical to the first. The first of this pattern will be to remove the diffraction effects in the phase conjugate field that resulted from the reference electrical signal. The result is a phase conjugate version of the original undistorted field that was incident on the device back propagating from it. If the input was an undistorted plane wave, the output is an undistorted plane wave--the aberration is removed. Such a plane wave front propagating optical field will be focused by a spherical lens to a maximum intensity, diffraction limited spot. This peak is proportional to the auto correlation function peak.
The index pattern is moving and the intensity peak occurs when the pattern and phase conjugate reconstruction of the original pattern are spatially congruent. As the index pattern moves across the reconstruction other intensity values corresponding to values of the autocorrelation as a function of the relative shift appear. The autocorrelation function is thus generated. For signals which are different the crosscorrelation function is generated.